Top 12 Quotes by Felix Klein

The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure.

The greatest mathematicians, as Archimedes, Newton, and Gauss, always united theory and applications in equal measure.

Newton, Theory, Mathematician

Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions.

Felix Klein

Confused, Math, Numbers

Mathematics in general is fundamentally the science of self-evident things.

Felix Klein

Self, Mathematics, Evident

"Anwendung der Differential-und Integralrechnung auf Geometrie". Book by Georg Scheffers, p. 26, 1920.

Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs.

Felix Klein

Math, Sensual, Intuition

Regarding the fundamental investigations of mathematics, there is no final ending ... no first beginning.

Felix Klein

Finals, Fundamentals, Firsts

The presentation of mathematics in schools should be psychological and not systematic. The teacher, so to speak, should be a diplomat. He must take account of the psychic processes in the boy in order to grip his interest, and he will succeed only if he presents things in a form intuitively comprehensible. A more abstract presentation is only possible in the upper classes.

Felix Klein

Teacher, School, Boys

It is well known that the central problem of the whole of modern mathematics is the study of transcendental functions defined by differential equations.

Felix Klein

Ontology, Logic, Study

Felix Klein (1893). “The Evanston Colloquium: Lectures on Mathematics Delivered from Aug. 28 to Sept. 9, 1893 Before Members of the Congress of Mathematics Held in Connection with the World's Fair in Chicago at Northwestern University, Evanston, Ill”

Every one who understands the subject will agree that even the basis on which the scientific explanation of nature rests is intelligible only to those who have learned at least the elements of the differential and integral calculus, as well as analytical geometry.

Felix Klein

Elements, Calculus, Geometry

Projective geometry has opened up for us with the greatest facility new territories in our science, and has rightly been called the royal road to our particular field of knowledge.

Felix Klein

Territory, Fields, Royal

The developing science departs at the same time more and more from its original scope and purpose and threatens to sacrifice its earlier unity and split into diverse branches.

Felix Klein

Sacrifice, Unity, Purpose

Felix Klein (1922). “Gesammelte mathematische Abhandlungen: Zur anschaulichen Geometrie. Zur Auflösung algebraischer Gleichungen. Physikalisches. Hrsg. von R. Fricke und H. Vermeil”

Among mathematicians in general, three main categories may be distinguished; and perhaps the names logicians, formalists, and intuitionists may serve to characterize them.

Felix Klein

Names, Three, May

Felix Klein (1893). “The Evanston Colloquium: Lectures on Mathematics Delivered from Aug. 28 to Sept. 9, 1893 Before Members of the Congress of Mathematics Held in Connection with the World's Fair in Chicago at Northwestern University, Evanston, Ill”

The teacher manages to get along still with the cumbersome algebraic analysis, in spite of its difficulties and imperfections, and avoids the smooth infinitesimal calculus, although the eighteenth century shyness toward it had long lost all point.

Felix Klein

Teacher, Science, Long

Felix Klein (2016). “Elementary Mathematics from a Higher Standpoint: Volume I: Arithmetic, Algebra, Analysis”, p.166, Springer